mathematics and Mathematicians. 1. The Concept of Mathematics. 2. A Mathematician's Life. 3. The Work of Mathematicians and the Mathematical Community. 4. Masters and Schools
II. The Nature of Mathematical Problems. 1. "Pure" Mathematics and "Applied" Mathematics. 2. Theoretical Physics and Mathematics. 3. Applications of Mathematics in the Classical Era. 4. The Utilitarian Attacks. 5. Fashionable Dogmas. 6. Conclusions
III. Objects and Methods in Classical Mathematics. 1. The Birth of Pre-Mathematical Ideas. 2. The Idea of Proof. 3. Axioms and Definitions. 4. Geometry, from Euclid to Hilbert. 5. Numbers and Magnitudes. 6. The Idea of Approximation. 7. The Evolution of Algebra. 8. The Method of Coordinates. 9. The Concept of Limit and the Infinitesimal Calculus
App. 1. Calculation of Ratios in Euclid's Book V
App. 2. The Axiomatic Theory of Real Numbers
App. 3. Approximation of the Real Roots of a Polynomial
App. 4. Arguments by "Exhaustion"
App. 5. Applications of Elementary Algorithms of the Integral Calculus
IV. Some Problems of Classical Mathematics. 1. Intractable Problems and Sterile Problems. 2. Prolific Problems
App. 1. Prime Numbers of the Form 4k-1 or 6k-1. App. 2. The Decomposition of [actual symbol not reproducible](s) as a Eulerian Product
App. 3. Lagrange's Method for the Solution of ax[superscript 2] + bxy + cy[superscript 2] = n in Integers
App. 4. Bernoulli Numbers and the Zeta Function
V. New Objects and New Methods. 1. New Calculations. 2. The First Structures. 3. The Language of Sets and General Structures. 4. Isomorphisms and Classifications. 5. Mathematics of Our Day. 6. Intuition and Structures
App. 1 The Resolution of Quartic Equations
App. 2 Additional Remarks on Groups and on the Resolution of Algebraic Equations
App. 3 Additional Remarks on Rings and Fields
App. 4. Examples of Distances
App. 5. Fourier Series
VI. Problems and Pseudo-Problems about "Foundations" 1. Non-Eueclidean Geometries. 2. The Deepening of the Concept of Number. 3. Infinite Sets. 4. "Paradoxes" and their Consequences. 5. The Rise of Mathematical Logic. 6. The Concept of "Rigorous Proof"
App. 1. Geometry on a Surface
App. 2. Models of the Real Numbers
App. 3. Theorems of Cantor and of his School

This book is of interest for students of mathematics or of neighboring subjects like physics, engineering, computer science, and also for people who have at least school level mathematics and have kept some interest in it. Also good for younger readers just reaching their final school year of mathematics.